SOLUTION: A farmer has 1000 feet of fence. He wants to enclose a pasture bordering on long straight river where no fence is needed. Find the area of the largest such enclosure.
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Question 255888: A farmer has 1000 feet of fence. He wants to enclose a pasture bordering on long straight river where no fence is needed. Find the area of the largest such enclosure.
Thank you for help. Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! We have two formulas:
(i) , where p =1000. Note we only have 3 sides.
(ii)
From (i) we get
(iii)
Solve (iii) for y to get
(iv)
substitute (iv) into (ii) to get
(v)
which is
(vi)
set -2x^2 + 1000x = 0 and create vertex form as
so the max area is 125,000 sq. ft.
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